Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.

Decentralised supply chain formation:a belief propagation-based approach

Decentralised supply chain formation involves determining the set of producers within a network able to supply goods to one or more consumers at the lowest cost. This problem is frequently tackled using auctions and negotiations. In this paper we show how it can be cast as an optimisation of a pairwise cost function. Optimising this class of functions is NP-hard but good approximations to the global minimum can be obtained using Loopy Belief Propagation (LBP). Here we detail a LBP-based approach to the supply chain formation problem, involving decentralised message-passing between potential participants. Our approach is evaluated against a well-known double-auction method and an optimal centralised technique, showing several improvements: it obtains better solutions for most networks that admit a competitive equilibrium Competitive equilibrium as defined in [3] is used as a means of classifying results on certain networks to allow for minor inefficiencies in their auction protocol and agent bidding strategies. while also solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions.

Decentralized supply chain formation using max-sum loopy belief propagation

Supply chain formation is the process by which a set of producers within a network determine the subset of these producers able to form a chain to supply goods to one or more consumers at the lowest cost. This problem has been tackled in a number of ways, including auctions, negotiations, and argumentation-based approaches. In this paper we show how this problem can be cast as an optimization of a pairwise cost function. Optimizing this class of energy functions is NP-hard but efficient approximations to the global minimum can be obtained using loopy belief propagation (LBP). Here we detail a max-sum LBP-based approach to the supply chain formation problem, involving decentralized message-passing between supply chain participants. Our approach is evaluated against a well-known decentralized double-auction method and an optimal centralized technique, showing several improvements on the auction method: it obtains better solutions for most network instances which allow for competitive equilibrium (Competitive equilibrium in Walsh and Wellman is a set of producer costs which permits a Pareto optimal state in which agents in the allocation receive non-negative surplus and agents not in the allocation would acquire non-positive surplus by participating in the supply chain) while also optimally solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions. © 2012 Wiley Periodicals, Inc.

Privatisation, state ownership and productivity:evidence from China

This paper examines the relationship between the transfer of ownership between the public and private sectors of Chinese industry, and its impacts on performance. We link ownership changes to productivity growth, and demonstrate that privatisation contributes significantly. We offer an extension that is generally ignored in the literature, in looking at firms that are taken back into state ownership, and evaluating the productivity growth effects of this. Further, we highlight the well-understood simultaneity problems, and demonstrate the hazard of ignoring the issue by comparing various estimators, including the modified control function approach. In general, the results stress the importance of allowing for such endogeneity when evaluating the productivity effects of ownership change.

Attention deficits in dyslexia:Evidence for an automatisation deficit?

Both attentional difficulties and rapid processing deficits have recently been linked with dyslexia. We report two studies comparing the performance of dyslexic and control teenagers on attentional tasks. The two studies were based on two different conceptions of attention. Study 1 employed a design that allowed three key components of attention - focusing, switching, and sustaining - to be investigated separately. One hypothesis under investigation was that rapid processing problems - in particular impaired ability to switch attention rapidly - might be associated with dyslexia. However, although dyslexic participants were significantly less accurate than their controls in a condition where they had to switch attention between two target types, the nature of the deficit suggested that the problem was not in switching attention per se. Thus, in Study 2, we explored an alternative interpretation of the Study 1 results in terms of the classic capacity-limited models of "central" attention. We contrasted two hypotheses: (1) that dyslexic teenagers have reduced cognitive resources versus (2) that they suffer from a general impairment in the ability to automatise basic skills. To investigate the automaticity of the shape recognition component of the task a similar attention paradigm to that used in Study 1 was employed, but using degraded, as well as intact, stimuli. It was found that stimulus degradation led to relatively less impairment for dyslexic than for matched control groups. The results support the hypothesis that dyslexic people suffer from a general impairment in the ability to automatise skills - in this case the skill of automatic shape recognition.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Application of the finite element method to problems in fracture mechanics

Numerical techniques have been finding increasing use in all aspects of fracture mechanics, and often provide the only means for analyzing fracture problems. The work presented here, is concerned with the application of the finite element method to cracked structures. The present work was directed towards the establishment of a comprehensive two-dimensional finite element, linear elastic, fracture analysis package. Significant progress has been made to this end, and features which can now be studied include multi-crack tip mixed-mode problems, involving partial crack closure. The crack tip core element was refined and special local crack tip elements were employed to reduce the element density in the neighbourhood of the core region. The work builds upon experience gained by previous research workers and, as part of the general development, the program was modified to incorporate the eight-node isoparametric quadrilateral element. Also. a more flexible solving routine was developed, and provided a very compact method of solving large sets of simultaneous equations, stored in a segmented form. To complement the finite element analysis programs, an automatic mesh generation program has been developed, which enables complex problems. involving fine element detail, to be investigated with a minimum of input data. The scheme has proven to be versati Ie and reasonably easy to implement. Numerous examples are given to demonstrate the accuracy and flexibility of the finite element technique.

Problem solving in architectural design

This thesis is presented in two parts. The first part is an attempt to set out a framework of factors influencing the problem solving stage of the architectural design process. The discussion covers the nature of architectural problems and some of the main ways in which they differ from other types of design problems. The structure of constraints that both the problem and the architect impose upon solutions are seen as of great importance in defining the type of design problem solving situation. The problem solver, or architect, is then studied. The literature of the psychology of thinking is surveyed for relevant work . All of the traditional schools of psychology are found wanting in terms of providing a comprehensive theory of thinking. Various types of thinking are examined, particularly structural and productive thought, for their relevance to design problem solving. Finally some reported common traits of architects are briefly reviewed. The second section is a report of u~o main experiments which model some aspects of architectural design problem solving. The first experiment examines the way in which architects come to understand the structure of their problems. The performances of first and final year architectural students are compared with those of postgraduate science students and sixth form pupils. On the whole these groups show significantly different results and also different cognitive strategies. The second experiment poses design problems which involve both subjective and objective criteria, and examines the way in which final year architectural students are able to relate the different types of constraint produced. In the final section the significance of all the results is suggested. Some educational and methodological implications are discussed and some further experiments and investigations are proposed.

Maintenance of communication in primary classrooms : some evidence for the role of elicitation and code-switching in English medium schools in Kenya, with implications for teaching

This is a study of specific aspects of classroom interaction primary school level in Kenya. The study entailed the identification of the sources of particular communication problems during the change-over period from Kiswahili to English medium teaching in two primary schools. There was subsequently an examination of the language resources which were employed by teachers to maintain pupil participation in communication in the light of the occurrence of possibility of occurrence of specific communication problems. The language resources which were found to be significant in this regard concerned firstly the use of different elicitation types by teachers to stimulate pupils into giving responses and secondly teachers' recourse to code-switching from English to Kiswahili and vice-versa. It was also found in this study that although the use of English as the medium of instruction in the classrooms which were observed resulted in certain communication problems, some of these problems need not have arisen if teachers had been more careful in their use of language. The consideration of this finding, after taking into account the role of different elicitation types and code-switching as interpretable from data samples had certain implications which are specified in the study for teaching in Kenyan primary schools. The corpus for the study consisted of audio-recordings of English, Science and Number-Work lessons which were later transcribed. Relevant data samples were subsequently extracted from transcripts for analysis. Many of the samples have examples of cases of communication breakdowns, but they also illustrate how teachers maintained interaction with pupils who had yet to acquire an operational mastery of English. This study thus differs from most studies on classroom interaction because of its basic concern with the examination of the resources available to teachers for overcoming the problem areas of classroom communication.

A systems and cybernetic perspective on complex problem solving

This thesis is concerned with Organisational Problem Solving. The work reflects the complexities of organisational problem situations and the eclectic approach that has been necessary to gain an understanding of the processes involved. The thesis is structured into three main parts. Part I describes the author's understanding of problems and suitable approaches. Chapter 2 identifies the Transcendental Realist (TR) view of science (Harre 1970, Bhaskar 1975) as the best general framework for identifying suitable approaches to complex organisational problems. Chapter 3 discusses the relationship between Checkland's methodology (1972) and TR. The need to generate iconic (explanatory) models of the problem situation is identified and the ability of viable system modelling to supplement the modelling stage of the methodology is explored in Chapter 4. Chapter 5 builds further on the methodology to produce an original iconic model of the methodological process. The model characterises the mechanisms of organisational problem situations as well as desirable procedural steps. The Weltanschauungen (W's) or "world views" of key actors is recognised as central to the mechanisms involved. Part II describes the experience which prompted the theoretical investigation. Chapter 6 describes the first year of the project. The success of this stage is attributed to the predominance of a single W. Chapter 7 describes the changes in the organisation which made the remaining phase of the project difficult. These difficulties are attributed to a failure to recognise the importance of differing W's. Part III revisits the theoretical and organisational issues. Chapter 8 identifies a range of techniques embodying W's which are compatible with .the framework of Part I and which might usefully supplement it. Chapter 9 characterises possible W's in the sponsoring organisation. Throughout the work, an attempt 1s made to reflect the process as well as the product of the author's leaving.

Minority influence and optimal problem-solving

An analogous thinking task was used to test Nemeth's Convergent–Divergent theory of majority and minority influence. Participants read a (base) problem and one of three solutions (one of which is considered the ‘best' solution). They then generated solutions to a second (target) problem which shared similar structural features to the first problem. Due to the similarities between problems, the solution given to the first problem can be used as an analogy in solving the second. In contrast to Nemeth's theory, when the solution to the base problem was endorsed by a numerical majority there was not an increase in analogy-transfer in solving the target problem. However, in support of Nemeth's theory, when the base solution was supported by a numerical minority then the participants were more likely to generate the ‘best' solution to the target problem regardless of which base solution they were given. Copyright © 1999 John Wiley & Sons, Ltd.

Attributions, cognitions, and coping styles:teleworkers' reactions to work-related problems

Based on the attributional reformulation of learned helplessness theory (Abramson, Seligman, & Teasdale, 1978) and Lazarus and Launier's (1978) primary-secondary appraisal theory of stress, the present study sought to examine teleworkers' reactions to their work-related problems. The role of attributions about the sources, and cognitions about the consesquences, of these problems in promoting positive adaptation was addressed. In particular, it was predicted that teleworkers who made optimistic attributions and cognitions would be more likely to employ problem-focused coping strategies and, as a result, report more positive psychological and job-related outcomes. Based on a survey sample of 192 teleworkers, the results indicated that a tendency to engage in self-blame was related to the use of emotion-focused coping strategies. In turn, there was evidence linking emotion-focused coping strategies to negative outcomes and problem-focused coping strategies to positive outcomes. The results are discussed in relation to attributional approaches to stress which highlight the importance of cognitions about the consequences of negative events. Finally, implications for the training of teleworkers are presented.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

An iterative procedure for solving a Cauchy problem for second order elliptic equations

An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.